lecture11 - EE 740 Professor Ali Keyhani Lecture#11...

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EE 740 Professor Ali Keyhani Lecture #11 Newton-Raphson Method
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Newton - Raphson Method Power Flow Problem: Given: P G i Sch , Q G i Sch Y Bus model Find: V Bus Plosses, Qlosses Pij, Qij Power flow through transmission lines and transformers Model: I Bus = Y Bus V Bus Ii = Σ YijVj for i = 1 to n Si = ViI*i 1 2 3
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Transmitted Power S Ti =P Ti + Q Ti = ViI* Ti for i = 1,2 but I T1 = Y 11 Y 12 V 1 I T2 Y 21 Y 22 V 2 or I Ti = Σ Yij Vj for i = 1,2 and j = 1,2 Let Vi = Vi ∠δ i Yij = Yij ∠γ ij Then I* Ti = Σ Yij Vj - γ ij - δ i for j = 1 to n S Ti = Vi Σ Yij Vj ∠δ i - δ j - γ ij for j = 1 to n Note that the net injection to bus (i) is: Pi inj = P G i Sch - P L i Sch Qi inj = Q G i Sch - Q L i Sch Therefore: Pi inj = P G i Sch - P L i Sch = Pi cal (V Bus , Y Bus ) Qi inj = Q G i Sch - Q L i Sch = Qi cal (V Bus , Y Bus ) Pi = Pi inj - Pi cal (V Bus , Y Bus ) ≤ε Qi = Qi inj - Qi cal (V Bus , Y Bus ) ≤ε Pi Qi i j
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Pi inj - Pi cal (V Bus , Y Bus ) = 0 Qi inj - Qi cal (V Bus , Y Bus ) = 0 i = 1,2… P1 inj - P1 cal (V 1 ,…V n ) = 0 f 1(X) = 0 Pi inj - Pi cal (V 1 ,…V n ) = 0 f i(X) = 0 Pn inj - Pn cal (V 1 ,…V n ) = 0 f n(X) = 0 f
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